PRP Records

Probable Primes Top 10000

(255244 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
8001(4^111231+23)/366968Robert Price02/2017
800216206^13549+13549^1620666962Hans Havermann08/2019
80032^222408-11127566952Enzo Doria05/2014
800410^66949-9^6694966949Jean-Louis Charton12/2005
80052^222378-100566943Lelio R Paula04/2012
8006(9*2^222366+1)/7366938Lelio R Paula08/2012
80077^79202-6^(79202+1)66934Robert Price06/2016
80082^222325-11225566927Enzo Doria06/2014
800921789^1178+1178^2178966918Hans Havermann08/2019
801020^51428+3366910Lelio R Paula08/2013
80112^222224-1850966897Enzo Doria05/2013
8012(38*10^66896+187)/966897Robert Price11/2017
80132^222192-86968810566887Lelio R Paula02/2016
8014(19*10^66878-43)/366879Robert Price10/2017
801511^64219-6466878Lelio R Paula07/2013
80162^222151-1729566875Lelio R Paula04/2012
8017gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
80182^222085-11103166855Enzo Doria05/2014
80198*10^66848-1366849Robert Price05/2017
8020(3^140087+4)/1366838Lelio R Paula04/2012
8021(3^140102+4)/884360943766836Lelio R Paula04/2012
802219^52265+5266835Lelio R Paula08/2013
80232*10^66826-2766827Robert Price02/2017
80244*6^85867+566819Lelio R Paula09/2014
802511955^16384+266807Matt Stath12/2018
802615^56800+866802Lelio R Paula08/2013
8027(2^221891-2^110946+1)/56679611/2006
802810^66793+6944166794Patrick De Geest05/2013
802910^66793-6366793Robert Price05/2011
803035^43256-170466791Enzo Doria03/2013
80313^139976+2^(139976-1)66786Robert Price05/2016
803288769!6-4866786Robert Price08/2018
80337^79023-5466783Lelio R Paula06/2013
8034104^33109-10366782Norbert Schneider11/2016
8035(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
8036(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
80382^221768+18366759Lelio R Paula02/2012
8037gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
8039(154*10^66755-1)/966757Serge Batalov12/2014
804011^64097+4866751Lelio R Paula07/2013
8041(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
8042(19*10^66748+413)/966749Robert Price10/2017
8043(3*2^221696-1)/1366737Lelio R Paula01/2014
80448*6^85758-766734Lelio R Paula09/2014
8045135^31325+266733Lelio R Paula05/2013
8046(49*10^66729+41)/966730Robert Price07/2015
8047(349*10^66720-7)/966722Robert Price03/2017
8048(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
8049(25*10^66714+71)/366715Robert Price01/2017
805011^64061-78066713Enzo Doria11/2012
80517^78929+466703Lelio R Paula06/2013
805211^64048-93066700Enzo Doria11/2012
8053120^32079-11966699Norbert Schneider09/2018
80542*7^78921+566697Lelio R Paula09/2014
8055(25*2^221526+1)/40966685Lelio R Paula08/2012
805616330^12117+12117^1633066682Hans Havermann08/2019
8057(2^221509-1)/29239188166673Jens K. Andersen02/2009
80582^221479+7295366672Enzo Doria04/2016
806010^66666+27540366667Patrick De Geest03/2010
805916317^12182+12182^1631766667Hans Havermann08/2019
806110^66666-11552166666Patrick De Geest03/2010
8062(18*10^66657-81)/9966657Ray Chandler01/2011
80634*10^66653+2166654Robert Price08/2016
8064(10^66650+149)/366650Serge Batalov12/2014
80659^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
80662^221391-214566646Lelio R Paula04/2012
806722952^801+801^2295266645Hans Havermann08/2019
8068(5*10^66613-119)/366614Robert Price04/2016
80692^221273-11323366610Enzo Doria07/2014
80703^139571-4666593Lelio R Paula06/2013
8071(4*10^(2*33295)-2*(10^33295)+1)/366591Robert Price04/2018
80722^221181-86968810566583Lelio R Paula02/2016
8073(61*10^66575-7)/966576Ray Chandler02/2012
80742^221126+13366566Lelio R Paula02/2012
807512^61680+9166564Lelio R Paula07/2013
8076(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
8077(13*10^66551-73)/366552Robert Price12/2016
807811^63901-159066547Enzo Doria12/2012
807911^63901-150066547Enzo Doria12/2012
80806^85517+2366546Lelio R Paula07/2013
808117^54069-4066530Lelio R Paula08/2013
8082(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
8083(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
8085(2^221008-1017)/7853366526Lelio R Paula04/2012
80843^139432+2666526Lelio R Paula06/2013
8086((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
8087((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
80886^85481+8548166518Henri Lifchitz08/2014
8089(9179*2^220913-1)/39966503Lelio R Paula04/2015
809013^59687+6666488Lelio R Paula07/2013
8091(49*10^66485-31)/966486Robert Price07/2015
8092(46*10^66469+17)/966470Robert Price06/2015
80932^220790+9766465Lelio R Paula02/2012
8094(23*2^220790+1)/80766463Lelio R Paula06/2012
809540009^14441-10266460Enzo Doria07/2012
80962^220736-14366449Lelio R Paula02/2012
809761077!4-6466448Robert Price11/2019
8098(79*10^66447-97)/9966447Ray Chandler01/2011
809921235^1344+1344^2123566432Hans Havermann08/2019
81002^220675+6966430Lelio R Paula02/2012
810119049^3070+3070^1904966427Hans Havermann08/2019
810288323!6-1666419Robert Price08/2018
81032^220633-11138166418Enzo Doria05/2014
8104(2^220625-509203)/400032166409Lelio R Paula05/2012
81052^220596-1581366407Enzo Doria04/2013
8106(5*10^66394-17)/366395Serge Batalov05/2009
81072^220549-185917366392Enzo Doria04/2016
81082^220478-16166371Lelio R Paula02/2012
81095^94938-1463666359Enzo Doria02/2013
8110(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
811115444^15839-15839^1544466346Norbert Schneider08/2018
81122^220253-11487166303Enzo Doria05/2015
811312^61432+9566297Lelio R Paula07/2013
81142^220192-11156366285Enzo Doria05/2014
81152^220188-11144966284Enzo Doria05/2014
8116(4*10^66284+23)/966284Robert Price11/2014
811732501!2+266266Robert Price01/2015
8118(8*10^66261-101)/366262Robert Price10/2017
81191530*10^66254+R(66254)66258Patrick De Geest05/2016
8120(47^39623-1)/4666252Robert Price06/2014
81212^220044-9730566240Lelio R Paula04/2012
8122(77*10^66237-257)/966238Robert Price10/2017
812329^45285+266225Ray Chandler08/2011
812416711^9178+9178^1671166222Hans Havermann08/2019
812515^56289+3866202Lelio R Paula08/2013
81263^138749+9866201Lelio R Paula06/2013
8127(21*2^219912-1)/566201Lelio R Paula01/2014
81292^219904-1699566198Lelio R Paula10/2011
81282^219903-461566198Yves Minet05/2019
8130(3^138712-2)/529766179Lelio R Paula04/2012
8131Phi(198552,10)66177Ray Chandler07/2010
81324*6^85041+766176Lelio R Paula09/2014
813316777^8794+8794^1677766172Hans Havermann08/2019
81342^219812-314966171Yves Minet10/2009
81352^219795-61116766165Paul Bourdelais03/2013
813632455!2+51266162Robert Price02/2015
8137(27*2^219760-1)/22766154Lelio R Paula01/2014
8139(11^63521-4^63521)/766150Robert Price03/2013
81385*7^78274-666150Lelio R Paula09/2014
814015853^14872+14872^1585366145Hans Havermann08/2019
8141(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
81422^219679-11201566130Enzo Doria05/2014
81432^219653+15015*21965366123Henri Lifchitz04/2005
814415445^15782-15782^1544566108Norbert Schneider08/2018
81452^219600+7656166107Enzo Doria05/2016
81462^219594+25525566105Lelio R Paula10/2011
81474*7^78210-366096Lelio R Paula09/2014
8148(15185*2^219557-1)/6366096Lelio R Paula04/2015
8149(19*2^219499-1)/1366076Lelio R Paula01/2014
81502^219496+6661566075Lelio R Paula10/2011
8151(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
815215871^14500+14500^1587166046Hans Havermann08/2019
8154(2^219414+7)/44365766045Lelio R Paula04/2012
8153(115*10^66043-1)/366045Serge Batalov12/2014
815510^66033+1966034Robert Price01/2011
815610^66033-7830966033Patrick De Geest05/2013
8157(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
81582^219304+45424566018Henri Lifchitz03/2007
8159(27*2^219293+1)/914566012Lelio R Paula08/2012
81602^219273-11263566008Enzo Doria06/2014
816117548^5771+5771^1754866003Hans Havermann08/2019
81622^219250+2566001Lelio R Paula08/2011
8163132^31123+13165999Norbert Schneider03/2015
816419327^2598+2598^1932765995Hans Havermann08/2019
816518440^3789+3789^1844065988Hans Havermann08/2019
8166V(319871)65987Serge Batalov03/2015
81672^219189-19565983Lelio R Paula08/2011
8168(7*2^219143-1)/5565968Lelio R Paula01/2014
8169(73^35401-1)/7265962Paul Bourdelais08/2017
81702^219112-1700965960Enzo Doria05/2013
81712^219093-11120165954Enzo Doria05/2014
81722^219089-11209965953Enzo Doria06/2014
817346714!3+8165950Robert Price09/2014
8174(11*10^65944-131)/365945Robert Price02/2017
81752^219021-355365932Yves Minet03/2017
8176Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
81772^218990+7351965923Enzo Doria04/2016
817858^37378-5765914Norbert Schneider09/2014
8180(2^218945-7)/167565906Lelio R Paula04/2012
81795*10^65905+8165906Robert Price08/2017
81813*10^65899-1365900Robert Price11/2017
8182(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
8183127^31322-265896Lelio R Paula10/2017
81842^218897-11188965895Enzo Doria05/2014
81852^218896+186945165895Enzo Doria05/2016
818663^36616+265885Lelio R Paula05/2013
8187(3*2^218822-1)/1165872Lelio R Paula01/2014
81882^218796-11329765865Enzo Doria07/2014
81892^218797+7372765865Enzo Doria04/2016
81903^138040-11065862Lelio R Paula06/2013
819111^63240-195065858Enzo Doria12/2012
81922^218764-11187365855Enzo Doria05/2014
8193(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
81943^137988+2665838Lelio R Paula06/2013
81952^218680-71965830Yves Minet05/2012
819618^52424+1765807Lelio R Paula08/2013
819719062^2827+2827^1906265790Hans Havermann08/2019
8198(2*15683^15683+1)/73238442565789David Broadhurst09/2010
8199(23*2^218517+1)/1900365778Lelio R Paula07/2012
8200(5*10^65773+1)/365774Erik Branger12/2013
8201160^29839-15965769Norbert Schneider12/2018
82022^218457-1732965763Enzo Doria05/2013
8203151703#+22338165759Nicolas PALAU10/2016
82042^218436+4075565756Lelio R Paula10/2011
82052^218399-462765745Yves Minet05/2019
8206(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
820715952^13219+13219^1595265742Hans Havermann08/2019
8208157^29934+29934^15765733Serge Batalov05/2014
8209211^28273-265715Lelio R Paula09/2013
8210(59*10^65712+31)/965713Robert Price09/2015
8211611^23586+23586^61165712Norbert Schneider08/2016
8212p(13991)#/2+3265712Robert Price12/2016
821315865^13864+13864^1586565712Hans Havermann07/2019
82142^218282-1848565710Enzo Doria05/2013
82152^218274-11125165708Enzo Doria05/2014
82162*F(314335)-165693Henri Lifchitz12/2009
82172^218200+42765685Henri Lifchitz01/2005
8218(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
8219(10199^(2^14)+(10197)^(2^14))/265676Robert Price05/2018
822046532!3+365667Robert Price10/2014
82212^218120-14765661Lelio R Paula08/2011
8222452^24729+24729^45265659Norbert Schneider09/2016
82235817^17440+17440^581765657Norbert Schneider06/2019
82242^218102-11489365656Enzo Doria05/2015
8225(15*2^218083-1)/1765650Lelio R Paula01/2014
8226(15*2^218081+1)/1894165646Lelio R Paula08/2012
822715818^14115+14115^1581865640Hans Havermann08/2019
8228(306^26407-1)/30565638Eric Chen09/2017
823019^51326+3665634Lelio R Paula08/2013
8229(21*2^218045-1)/45158365634Lelio R Paula01/2014
82312^217989-3365622Lelio R Paula08/2011
8232(13*2^217961+1)/365614Lelio R Paula06/2012
82334*6^84315-565611Lelio R Paula09/2014
8234(315047^11933+1)/31504865607Faysal YAtim06/2008
82356^84303+5565601Lelio R Paula07/2013
823616585^9024+9024^1658565601Hans Havermann08/2019
823718462^3575+3575^1846265601Hans Havermann08/2019
823815963^12862+12862^1596365597Hans Havermann08/2019
8239(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
8240(9787*2^217873-1)/3765589Lelio R Paula04/2015
82415*2^217858+365583Lelio R Paula04/2014
8242(19*10^65572+119)/365573Robert Price02/2017
824420^50399+5165571Lelio R Paula08/2013
82437162^17009+17009^716265571Norbert Schneider07/2018
824511^62946-567065552Enzo Doria01/2013
82462^217742-391165547Yves Minet08/2009
8247(19*10^65545+77)/365546Robert Price08/2016
82482^217731+13165544Lelio R Paula08/2011
82492^217720-11128765541Enzo Doria05/2014
8250(365^25579+1)/36665539Eric Chen10/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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